%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU953^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:29:38 AM UTC 2026
% Result : Theorem 3.54s 2.28s
% Output : Refutation 3.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 17 ( 10 unt; 0 typ; 1 def)
% Number of atoms : 29 ( 28 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 70 ( 13 ~; 4 |; 1 &; 46 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 42 ( 14 ^; 23 !; 4 ?; 42 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(g_decl,type,
g: $i > $i ).
thf(sk1_decl,type,
sk1: $i > $i ).
thf(sk2_decl,type,
sk2: ( $i > $i ) > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $i] :
! [B: $i] :
( ( A @ ( g @ B ) )
= B ) ) ) ).
thf(1,conjecture,
( ! [A: $i,B: $i] :
( ( ( g @ A )
= ( g @ B ) )
=> ( A = B ) )
=> ? [A: $i > $i] :
( ( ^ [B: $i] : ( A @ ( g @ B ) ) )
= ( ^ [B: $i] : B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM591_pme) ).
thf(2,negated_conjecture,
~ ( ! [A: $i,B: $i] :
( ( ( g @ A )
= ( g @ B ) )
=> ( A = B ) )
=> ? [A: $i > $i] :
( ( ^ [B: $i] : ( A @ ( g @ B ) ) )
= ( ^ [B: $i] : B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] :
( ( ( g @ A )
= ( g @ B ) )
=> ( A = B ) )
=> ? [A: $i > $i] :
( ( ^ [B: $i] : ( A @ ( g @ B ) ) )
= ( ^ [B: $i] : B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [C: $i > $i,B: $i,A: $i] :
( ( ( ( g @ A )
!= ( g @ B ) )
| ( A = B ) )
& ( ( ^ [D: $i] : ( C @ ( g @ D ) ) )
!= ( ^ [D: $i] : D ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [B: $i,A: $i] :
( ( ( g @ A )
!= ( g @ B ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
! [B: $i,A: $i] :
( ( ( g @ A )
!= ( g @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(8,plain,
? [A: $i > $i] :
! [B: $i] :
( ( A @ ( g @ B ) )
= B ),
inference(detectInverse,[status(thm)],[7]) ).
thf(9,plain,
! [A: $i] :
( ( sk1 @ ( g @ A ) )
= A ),
inference(cnf,[status(esa)],[8]) ).
thf(13,plain,
! [A: $i] :
( ( sk1 @ ( g @ A ) )
= A ),
inference(lifteq,[status(thm)],[9]) ).
thf(6,plain,
! [A: $i > $i] :
( ( ^ [B: $i] : ( A @ ( g @ B ) ) )
!= ( ^ [B: $i] : B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(10,plain,
! [A: $i > $i] :
( ( ^ [B: $i] : ( A @ ( g @ B ) ) )
!= ( ^ [B: $i] : B ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(11,plain,
! [A: $i > $i] :
( ( ^ [B: $i] : ( A @ ( g @ B ) ) )
!= ( ^ [B: $i] : B ) ),
inference(simp,[status(thm)],[10]) ).
thf(12,plain,
! [A: $i > $i] :
( ( A @ ( g @ ( sk2 @ A ) ) )
!= ( sk2 @ A ) ),
inference(func_ext,[status(esa)],[11]) ).
thf(14,plain,
! [B: $i > $i,A: $i] :
( ( A
!= ( sk2 @ B ) )
| ( ( sk1 @ ( g @ A ) )
!= ( B @ ( g @ ( sk2 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,12]) ).
thf(16,plain,
( ( sk2 @ sk1 )
!= ( sk2 @ sk1 ) ),
inference(pre_uni,[status(thm)],[14:[bind(A,$thf( sk2 @ sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(17,plain,
$false,
inference(pattern_uni,[status(thm)],[16:[]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU953^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.20 % Computer : n019.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 14:50:48 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.88/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.19/0.97 % [INFO] Parsing done (180ms).
% 1.19/0.98 % [INFO] Running in sequential loop mode.
% 1.74/1.37 % [INFO] eprover registered as external prover.
% 1.74/1.37 % [INFO] Scanning for conjecture ...
% 1.92/1.46 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.08/1.50 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.08/1.50 % [INFO] Problem is higher-order (TPTP THF).
% 2.08/1.50 % [INFO] Type checking passed.
% 2.08/1.51 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 3.54/2.28 % [INFO] Killing All external provers ...
% 3.54/2.28 % Time passed: 1940ms (effective reasoning time: 1289ms)
% 3.54/2.28 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 3.54/2.28 % Axioms used in derivation (0):
% 3.54/2.28 % No. of inferences in proof: 16
% 3.54/2.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1940 ms resp. 1289 ms w/o parsing
% 3.74/2.33 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.74/2.33 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------